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How AD can help solve differential-algebraic equations

Pryce, John, Nedialkov, Nedialko S., Tan, Guangning and Li, Xiao 2018. How AD can help solve differential-algebraic equations. Optimization Methods and Software 10.1080/10556788.2018.1428605

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Abstract

A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of the so-called index reduction or regularization, to prepare them for numerical solution. This is often done with the help of a computer algebra system. We show in two significant cases that it can be done efficiently by pure algorithmic differentiation. The first is the Dummy Derivatives method; here we give a mainly theoretical description, with tutorial examples. The second is the solution of a mechanical system directly from its Lagrangian formulation. Here, we outline the theory and show several non-trivial examples of using the ‘Lagrangian facility’ of the Nedialkov– Pryce initial-value solver DAETS, namely a spring-mass-multi-pendulum system; a prescribed-trajectory control problem; and long-time integration of a model of the outer planets of the solar system, taken from the DETEST testing package for ODE solvers.

Item Type: Article
Date Type: Published Online
Status: Published
Schools: Mathematics
Publisher: Taylor and Francis
ISSN: 1055-6788
Funders: Leverhulme Trust; NSERC Canada
Date of First Compliant Deposit: 28 March 2018
Date of Acceptance: 10 January 2018
Last Modified: 30 Jun 2019 13:11
URI: http://orca.cf.ac.uk/id/eprint/110289

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